To factor the expression \(12y + 6\) using the greatest common factor (GCF), we first find the GCF of the coefficients 12 and 6.
The GCF of 12 and 6 is 6.
Now, we can factor out 6 from the expression:
\[ 12y + 6 = 6(2y + 1) \]
Thus, the factored form of \(12y + 6\) is:
\[ \boxed{6(2y + 1)} \]